Question

$20$ teachers of a school teach either mathematics or physics. $12$ of them teach mathematics while $4$ teach both the subjects. Then number of teacher teaching only physics is

• A. $12$
• B. $8$
• C. $6$
• D. none of these

Answer 1

The correct option is A $12$

Total number of teachers$=20$

Let

$\text{A=no. of teacher teaches maths=12}$

$\text{B=no. of teacher teaches physics=n}$

$\text{C=no. of teacher teaches maths or physics=4}$

Hence,

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$⟹n\left(B\right)=20-12+4=12$

So, the number of teachers teaches physics only is $12$.